FORECASTING. Methods and Applications. Third Edition. Spyros Makridakis. European Institute of Business Administration (INSEAD) Steven C Wheelwright

Transcription

1 FORECASTING Methods and Applications Third Edition Spyros Makridakis European Institute of Business Administration (INSEAD) Steven C Wheelwright Harvard University, Graduate School of Business Administration Rob J. Hyndman Monash University, Department of Mathematics and Statistics Technische University Darmstadt Fachbereich 1 Betriebswirtschaftliche Bibiiothek Inventar-Nr. Abstell-Nr.: John Wiley & Sons, Inc.

2 CONTENTS 1 / THE FORECASTING PERSPECTIVE 1/1 Why forecast? 2 1/2 An overview of forecasting techniques 6 1/2/1 Explanatory versus time series forecasting 10 1/2/2 Qualitative forecasting 12 1/3 The basic steps in a forecasting task 13 bibliography 17 Exercises 19 2 / BASIC FORECASTING TOOLS 20 2/1 Time series and cross-sectional data 21. 2/2 Graphical summaries 23 2/2/1 Time plots and time series patterns 24 2/2/2 Seasonal plots 26 2/2/3 Scatterplots 27 2/3 Numerical summaries 28 2/3/1 Univariate statistics 29 2/3/2 Bivariate statistics 34 2/3/3 Autocorrelation 38 2/4 Measuring forecast accuracy 41 2/4/1 Standard statistical measures 42 2/4/2 Out-of-sample accuracy measurement 45 2/4/3 Comparing forecast methods 46 2/4/4 Theirs U-statistic 48 2/4/5 ACF of forecast error 50 I 2/5 Prediction intervals 52 2/6 Least SQuares estimates 54 2/6/1 Discovering and describing relationships 59 2/7 Transformations and adjustments 63 2/7/1 Mathematical transformations 63 2/7/2 Calendar adjustments 67 2/7/3 Adjustments for inflation and population changes 70 Appendices 71 2-A Notation for Quantitative forecasting 71 2-B Summation sign X 72 bibliography 74 Exercises 76 3/ TIME SERIES DECOMPOSITION 81 3/1 Principles of decomposition 84 3/1/1 Decomposition models 84 3/1/2 Decomposition graphics 87 3/1/3 Seasonal adjustment 88 3/2 Moving averages 89 3/2/1 Simple moving averages 89 3/2/2 Centered moving averages 94 3/2/3 Double moving averages 98 3/2/4 Weighted moving averages 98 3/3 Local regression smoothing 101 3/3/1 Loess 104 3/4 Classical decomposition 106 3/4/1 Additive decomposition 107 3/4/2 Multiplicative decomposition 109 IX

3 3 A H S 3 3/4/3 Variations on classical decomposition 112 3/5 Census Bureau methods 113 3/5/1 First Iteration 114 3/5/2 Later iterations 118 3/5/3 Extensions to X-I2-AR1MA 119 3/6 STL decomposition 121 3/6/1 Inner loop 122 3/6/2 Outer loop 123 3/6/3 Choosing the STL parameters 124 3/6/4 Comparing STL with X-12-ARIMA 124 3/7 Forecasting and decomposition 125 bibliography 127 Exercises 130 4/ EXPONENTIAL SMOOTHING METHODS 135 4/1 The forecasting scenario 138 4/2 Averaging methods 141 4/2/1 The mean 141 4/2/2 Moving averages 142 4/3 Exponential smoothing methods 147 4/3/1 Single exponential smoothing 147 4/3/2 Single exponential smoothing: an adaptive approach 155 4/3/3 Hot's linear method 158 4/3/4 Holt-Winters' trend and seasonally method 161 4/3/5 Exponential smoothing: Pegels' classification 169 4/4 A comparison of methods 171 4/5 General aspects of smoothing - methods 174 4/5/1 Initialization 174 4/S/2 Optimization 176 4/5/3 Prediction intervals 177 bibliography 179 Exercises 181 5/ SIMPLE REGRESSION 185 5/1 Regression methods 186 5/2 Simple regression 187 5/2/1 Least souares estimation 188 5/2/2 The correlation coefficient 193 S/2/3 Cautions In using correlation 196 5/2/4 Simple regression and the correlation coefficient 198 5/2/5 Residuals, outliers, and Influential observations 203 5/2/6 Correlation and causation 208 5/3 Inference and forecasting with simple regression 208 5/3/1 Regression as statistical modeling 209 5/3/2 The F-test for overall significance 211 5/3/3 Confidence Intervals for individual coefficients 215' 5/3/4 Mests for Individual coefficients 217 5/3/5 Forecasting using the simple regression model 218 5/4 Non-linear relationships 221 5/4/1 Non-linearity In the parameters 222 5/4/2 Using logarithms to form linear models 224 5/4/3 Local regression 224 Appendixes A Determining the values of o and b 228

4 bibliography 230 Exercises 231 6/ MULTIPLE REGRESSION 240 6/1 6/2 6/3 6/4 6/5 Introduction to multiple linear regression 241 6/1/1 Multiple regression model: theory and practice 248 6//I/2 Solving for the regression coefficients 250 6/1/3 Multiple regression and the coefficient of determination 6/1/4 The F-test for overall 6/1/5 251 significance 252 Individual coefficients: confidence intervals and f-tests 255 6/1/6 The assumptions behind multiple linear regression models 259 Regression with time series 263 6/2/1 Checking independence of residuals 265 6/2/2 Time-related explanatory variables 269 Selecting variables 274-* 6/3/1 The long list 276 6/3/2 The short list 277 6/3/3 Best subsets regression 279 6/3/4 Stepwise regression 285 Multicollinearity 287 6/4/1 Multicollinearity when there are two regressors 289 6/4/2 Multicollinearity when there are more than two regressors 289 Multiple regression and forecasting 291 6/6 Econometric models 299 6/6/1 The basis of econometric modeling 299 6/6/2 The advantages and drawbacks of econometric methods 301 Appendixes A The Durbln-Watson statistic 303 bibliography 305 Exercises 306 7/ THE BOX-JENKINS 7/1 7/2 6/5/1 Example: cross-sectional 7/3 regression and forecasting 292 6/5/2 Example: time series regression and forecasting 294 6/5/3 Recapitulation 298 METHODOLOGY FOR ARIMA MODELS 311 Examining correlations in times series data 313 7/1/1 The autocorrelation function 313 7/1/2 A white noise model 317 7/1/3 The sampling distribution of autocorrelations 317 7/1/4 Portmanteau tests 318 7/1/5 The partial autocorrelation coefficient 320 7/1/6 Recognizing-seasonality in a time series 322 7/1/7 Example: Pigs slaughtered 322 Examining stationarity of time series data 324 7/2/1 Removing non-statlonarlty in a time series 326 7/2/2 A random walk model 329 7/2/3 Tests for statationarlty 329 7/2/4 Seasonal differencing 331 7/2/5 Backshlft notion 334 ARIMA models for times series data 335 7/3/1 An autoregressive model of order one 337 xi

5 3; N s 7/3/2 A moving average model of order one 339 7/3/3 Higher-order autoregressive models 339 7/3/4 Higher-order moving average models 342 7/3/5 Mixtures: ARIMA models 344 7/3/6 Mixtures: ARIMA models 345 7/3/7 Seasonally and ARIMA models 346 7/4 Identification 347 7/4/1 Example I: A non-seasonal time series 349 7/4/2 Example 2: A seasonal time series 352 7/4/3 Example 3: A seasonal time series needing transformation 354 7/4/4 Recapitulation 357 7/5 Estimating the parameters 358 7/6 Identification revisited 360 7/6/1 Example 1: Internet usage 362 7/6/2 Example 2: Sales of printing/ writing paper 362 7/7 Diagnostic checking 364 7/& Forecasting with ARIMA.. models 366 7/8/1 Point forecasts 366 7/8/2 Out-of-sample forecasting 370 7/8/3 The effect of differencing on forecasts 371 7/8/4 ARIMA models used in time series decomposition 372 7/8/5 Eoulvalances with exponential smoothing models 373 bibliography 374 Exercises / ADVANCED FORECASTING MODELS 388 8/1 Regression with ARIMA errors 390 8/1/1 Modeling procedure 391 8/1/2 Example: Japanese motor vehicle production 393 8/1/3 Example: Sales of petroleum and coal products 396 8/1/4 Forecasting 400 8/2 Dynamic regression models 403 8/2/1 Lagged explanatory variables 403 8/2/2 Kqyck model 406 8/2/3 The basic forms of the dynamic regression model 407 8/2/4 Selecting the model order 409 8/2/5 Forecasting 413 8/2/6 Example: Housing starts 415 8/3 Intervention analysis 418 8/3/1 Step-based Interventions 419 8/3/2 Pulse-based Interventions 421 8/3/3 Further reading 422 8/3/4 Intervention models and forecasting 423 8/4 Multivariate autoregressive models 423 8/5 State space models 429 8/5/1 Some forecasting models in state space form 429 8/5/2 State space forecasting 431 8/5/3 The value of state space models 433 8/6 Non-linear models 433 8/7 Neural network forecasting 435 Xli

6 bibliography 440 Exercises 444 9/ FORECASTING THE LONG- TERM 451 9/1 Cycles versus long-term trends: forecasting copper prices 452 9/1/1 Forecasting IBM's sales 457 9/2 Long-term mega economic trends 459 9/2/1 Cycles of various durations and depths 461 9/2/2 Implications of extrapolating long-term trends 464 9/3 Analogies 466 9/3/1 The Information versus the Industrial Revolution 467 9/3/2 Five major inventions of the Industrial Revolution and their analogs 469 9/4 Scenario building 472 9/4/1 Businesses: gaining and/o*r maintaining competitive advantages 472 9/4/2 Jobs, work, and leisure time 475 9/4/3 Physical versus tele-interactions: extent and speed of acceptance 476 bibliography 478 Exercises / JUDGMENTAL FORECASTING AND ADJUSTMENTS /1 The accuracy of judgmental forecasts /1/1 The accuracy of forecasts in financial and other markets /1/2 Non-Investment type forecasts /2 The nature of judgmental biases and limitations /2/1 ludgmental biases in forecasting /2/2 Dealing with judgmental biases /2/3 Conventional wisdom /3 Combining statistical and judgmental forecasts /3/1 Arriving at final forecasts during a budget meeting /4 Conclusion 508 bibliography 509 Exercises / THE USE OF FORECASTING I I/I METHODS IN PRACTICE 514 Surveys among forecasting users 515 I I/I/I Familiarity and satisfaction with major forecasting methods /1/2 The use of different forecasting methods /2 Post-sample accuracy: empirical findings /3 Factors influencing method selection /4 The combination of forecasts /4/1 Factors that contribute to making combining work /4/2 An example of combining 539 xill

7 bibliography 543 Exercises /IMPLEMENTING FORECASTING: ITS USES, ADVANTAGES, AND LIMITATIONS /1 What can and cannot be predicted /1/1 Short-term predictions /1/2 Medium-term predictions /1/3 Long-term predictions /2 Organizational aspects of forecasting /2/1 Correcting an organization's forecasting problems /2/2 Types of forecasting problems and their solutions /3 Extrapolative predictions versus creative insights /3/1 Hindsight versus foresight -S69 12/4 Forecasting in the future /4/1 Data, Information, and forecasts 571 ' 12/4/2 Collective knowledge, experience, and forecasting 572 bibliography 575 Exercises 576 APPENDIX 1 / FORECASTING RESOURCES 577 I Forecasting software 578 1/1 Spreadsheets 578 1/2 Statistics packages 578 1/3 Specialty forecasting packages 579 1/4 Selecting a forecasting package Forecasting associations Forecasting conferences Forecasting journals and newsletters Forecasting on the Internet 586 bibliography 588 APPENDIX II / GLOSSARY OF FORECASTING TERMS 589 APPENDIX III / STATISTICAL TABLES 549 A: Normal probabilities 620 B: Critical values for t-statistic 621 C: Critical values for F-statistic 622 D: Inverse normal table 628 E: Critical values for x 2 statistic 629 F: Values of the Durbin-Watson statistic 630 G: Normally distributed observations 632 AUTHOR INDEX 633 SUBIECT INDEX 636 xlv